This invention relates to bandgap references, to bandgap references fabricated as monolithic integrated circuits and, in particular, to a correction circuit for the nonlinear, TlnT error term associated with such bandgap references.
Various systems, such as A/D converters, D/A converters, temperature sensors, measurement systems and voltage regulators use reference circuits to establish accuracy of the system. Typically, the reference is one of two types, a bandgap reference or a zener reference.
Zener diode references require a voltage of perhaps 10 volts to achieve the proper operating range relative to the breakdown voltage of approximately seven volts. However, the trend in the microelectronics industry is to decrease the power supply voltage and to standardize on a single five-volt supply. The effect is to decrease the number of applications for which zener references are suitable. At the same time, the need is for an accurate reference. It is believed that bandgap references are the principal circuits of this type capable of satisfying the dual requirements of accuracy and operating on a single, five-volt supply. However, the requirement for accuracy in the bandgap reference translates into an increasingly stringent requirement of predictable linearity in the temperature coefficient.
At this point, it will be helpful to review the features of a state-of-the-art conventional bandgap reference and an approximation for its output. FIG. 1 schematically illustrates such a reference, in the form of the relatively simple, yet relatively accurate bandgap reference circuit 10 which is the Brokaw cell.
In the Brokaw cell 10, the values of resistors R1 and R2 and the operational amplifier A1 are configured to force NPN transistors Q1 and Q2 to operate at equal collector current levels. Secondly, the ratio, A, of the emitter-junction area of Q1 and Q2 is a value such as 10, so that when Q1 and Q2 are operating at equal collector current levels, the base-emitter voltage, V.sub.Be, of Q1 will be a predetermined lesser value that the base-emitter voltage of Q2. Third, the voltage drop across R3, V.sub.R3, is simply .DELTA.V.sub.Be, the difference between the base-emitter voltages of transistors Q1 and Q2. As is well known, such a differential voltage is proportional to absolute temperature, that is, it is a "PTAT" voltage, and is of the form: ##EQU1## where A is the selected current density ratio of Q1 and Q2 or, equivalently, is the ratio of the emitter-junction areas of Q1 and Q2, since they are operating at equal current levels. Fourth, because i.sub.4 =i.sub.1 +i.sub.2 =2i.sub.2, the ratio of the voltage drops V.sub.R4 /V.sub.R3 for the resistor voltage divider R4 and R3 is given by G=V.sub.R4 /V.sub.R3 =2R4/R3.
Also the reference output voltage V.sub.OUT at the base of transistor Q2 is the sum of V.sub.Be the base-emitter voltage for Q2 and of V.sub.R4. Since V.sub.R4 is a multiple of V.sub.R3, and since V.sub.R3 is a temperature-dependent (PTAT) voltage, V.sub.OUT can be expressed as ##EQU2##
In practice, at least as a first approximation, a relatively accurate, stable reference output voltage V.sub.OUT can be obtained if the ratio of R.sub.4 /R.sub.3 is selected such that the positive temperature coefficient of the second term of (2) matches, and therefore cancels, the negative temperature coefficient of the first term (V.sub.Be).
Despite the relatively accurate output obtained with the above-described circuit, there are potentially two sources of temperature-induced curvature in the output of bandgap references.
The first source relates to the use of diffused resistors in bandgap references. Diffused resistors have a very high temperature coefficient, in the order of 1000 to 3000 PPM/.degree.C., which translates into a substantial curvature in the reference voltage. However, the nonlinearity associated with resistors can be eliminated to a great extent by the use of thin film resistors, such as nichrome or sichrome resistors, which have a much lower temperature coefficient.
A second, currently more difficult source of nonlinearity in bandgap references results from an inherent error term of the general form TlnT. This error is evidenced in the complete expression for the output voltage of a bandgap voltage reference, which is: ##EQU3## The temperature coefficient is obtained by taking the derivative with respect to temperature: ##EQU4## where: C.sub.1 =constant,
K=Boltzmann's constant, PA0 q=charge on electron, PA0 V.sub.go =extrapolated bandgap voltage of silicon, PA0 T.sub.o =temperature at which V.sub.Beo is measured, PA0 V.sub.Beo =base emitter voltage of a silicon transistor measured at a collector current of Ico at temperature To, PA0 Ic=collector operating current of transistor (nominally a function of temperature), PA0 n=constant, .about.2, and PA0 T=Kelvin temperature.
All the terms in the derivative except the last two are independent of temperature. In practice, the sum of all terms can be made equal to zero at room temperature to approximate zero temperature coefficient in the reference. Because of the last two terms, however, the temperature coefficient would still not be zero at all temperatures.
Specifically, consider (nK/q)ln(T/T.sub.o), the next to the last term of equation (4). At -55.degree. C., 25.degree. C., and 125.degree. C., this term takes on values -49 .mu.V/.degree.C., 0, and +49 .mu.V/.degree.C. This represents a 98 .mu.V/.degree.C. shift in the reference temperature coefficient over the range -55.degree. C. to +125.degree. C. The reference voltage itself is approximately 1.2 volts, which yields a shift in reference drift of approximately 82 ppM/.degree.C., and limits the usefulness of the basic bandgap in high accuracy, wide temperature range applications.
The second nonlinear term, (K/q)ln(I.sub.c /I.sub.co) can be used to cancel the first nonlinear term, because the signs are reversed. Total cancellation would occur when I.sub.c =I.sub.co (T/T.sub.o).sup.n. This power expression for the operating current of the transistor is one way of correcting the nonlinearity of a bandgap reference, but the circuit required to implement the correction is complicated and the widely varying operating current can present problems for circuit operation.
A parabolic correction circuit is used in the temperature sensor circuit described by Pease, in a paper entitled "A New Celsius Temperature Sensor", published and presented at the Circuits and Systems Conference, May 1, 1982, in Pasadena, Calif. The sensor uses a T.sub.2 generator circuit developed by applicant to correct for the TlnT nonlinearity term. The T.sup.2 generator circuit is shown as system 20 in FIG. 2. Briefly stated, a current which is proportional to absolute temperature (IPTAT) is fed through the transistors Q1 and Q2 whereas the current summed into Q3 is constant versus temperature. The relationships are such that the correction current I4 through Q4 is a product (I.sub.1 .times.I.sub.2)/I.sub.3, where I.sub.1 and I.sub.2 are the IPTAT's through Q1 and Q2 and I.sub.3 is the current across Q3. That is, I.sub.4 .about.IPTAT.sup.2 .about.T.sup.2. This T.sup.2 curvature compensation circuit is designed to be added to the temperature sensor circuit. It should be noted, however, that the T.sup.2 curvature compensation circuit 20 is not a true bandgap correction circuit. While the circuit 20 is the simplest, perhaps most effective T.sub.2 temperature curvature compensation circuit of which applicant is aware and while the T.sup.2 term does approximate the error term of bandgap references, bandgap references nonetheless deviate from the T.sup.2 term, especially at lower temperatures. As a result, a much better overall correction for bandgap nonlinearity would be provided by using a real TlnT term.
Unfortunately, very little has been done to address the nonlinearity problem. The only known exception, in which a circuit has been used to generate a TlnT term involves an A/D converter, with bandgap reference and correction circuit. The correction circuit is complex and, essentially irrelevant to the relatively simple yet effective curvature correction circuit which is the object of the present invention.
Thus, with few exceptions, curvature correction techniques are not available for bandgap references. This is unfortunate: the nonlinear TlnT error term limits the minimum temperature coefficient obtainable with the reference because the temperature coefficient itself is thus a function of temperature. Significant improvement in bandgap reference performance with regard to temperature drift will be achieved by eliminating this nonlinear term.